y^2+2=x^2-2

解答

y^{2} + 2 = x^{2} - 2

(h, k) = (0, 0), a = 2, b = 2

求解步骤

y^{2} + 2 = x^{2} - 2

将

y^{2} + 2 - x^{2} + 2 = 0

改写为标准双曲线方程形式

\frac{( x - 0 ) ^{2}}{2 ^{2}} - \frac{( y - 0 ) ^{2}}{2 ^{2}} = 1

因此双曲线的性质为:

(h, k) = (0, 0), a = 2, b = 2

3 x^{2} - 12 x - \frac{y ^{2}}{4} - \frac{y}{2} + \frac{43}{4} = 0

- x^{2} + 3 y^{2} - 4 x + 6 y = 28

\frac{y ^{2}}{1} - \frac{x ^{2}}{15} = 1

\frac{( x - 2 ) ^{2}}{36} - \frac{( y + 1 ) ^{2}}{64} = 1

- x^{2} + y^{2} = - 13